The present invention relates generally to magnetic resonance (MR) imaging, and more specifically, to a system and method for designing multi-channel and multi-dimensional spatially selective radio frequency (RF) pulse profiles using a linear approximation approach. By utilizing a linear class large tip angle approximation, it is possible to design RF pulses having non-uniform or non-separable flip angle profiles with arbitrarily large magnitudes. In addition, such an approach can account for arbitrary initial magnetizations,
MR imaging in general is based upon the principle of nuclear magnetic resonance. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field, such as a B1 excitation field, which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, or “longitudinal magnetization”, MZ, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated and this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received MR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
During a transmit sequence, an MR system will transmit RF pulses of given frequencies having particular profiles while various magnetic field gradients are being applied. For example, in a spin-echo based sequence, an MR system would transmit an excitation pulse at a particular frequency and transmit power for a particular time, in order to induce a net transverse magnetization in nuclei of a scan subject. Subsequent pulses transmitted by the system may have the same or a similar frequency, but might have different gain, amplitude, and duration attributes to cause a different change in magnetization (or “flip angle”) in order to cause spin echoes. Thus, in general, the particular shapes of the RF pulses in a transmit sequence are varied to manipulate the net magnetization in nuclei of the scan subject.
The attributes of RF pulses can be adjusted such that only spins within a given two dimensional (2 D) or three-dimensional (3 D) portion of a scan subject are affected. This is useful in such techniques as reduced field of view imaging or spatially-selective imaging. However, RF pulses which selectively excite nuclei in 2 D or 3 D locations can often have a long duration and/or a complex shape. The long duration tends to make the use of these conventionally-designed RF pulses inefficient or ineffective, due to phase accumulation from off resonant spins and T2 decay. Presently, multidimensional spatially-selective pulses are designed using approximation techniques, such as the small tip angle (STA) approximation, the linear class large tip angle (LCLTA) approximation, and techniques based upon echo planar imaging (EPI) trajectories.
The duration of multi-dimensional spatially-selective pulses can be decreased when multiple transmit channels are available, such as through parallel transmission. In parallel transmission, each coil exhibits a spatially different sensitivity pattern and is driven by an independently controlled RF waveform. Transmission time reduction is achieved by causing the pulses to undersample excitation k-space. One method of undersampling is known as “acceleration” of the pulses. For example, in a spiral k-space trajectory, an acceleration could be an increase in the distance between spiral turns of the trajectory. If no compensation is made for the undersampling, the resulting magnetization can be significantly degraded by aliasing caused by the excited field of view being too small. However, with multiple transmit channels, compensation for the acceleration is possible by including information from the spatial profile of the transmit coils in the design of the RF pulse in lieu of the omitted k-space information.
So far, parallel transmission has only been explored using pulses designed with the STA method. However, STA is limited to small tip angles and begins to produce significant error around 90 degrees. LCLTA and EPI-based approaches are generally used for larger tip angles. However, the feasibility of extending these methods to multiple transmission channels is so far unknown.
In addition, the EPI-based approaches are generally based on an assumption that the desired magnetization profile is separable, as is the case with cylindrical or square slab profiles. In other words, a multidimensional RF pulse can be designed using an EPI-based approach by designing lower dimensional pulses along different dimensions. For example, a 2 D pulse could be designed using 1 D sinc or Shinnar-Le Roux along each dimension. A 3 D pulse could be designed using combinations of 1 D and 2 D pulses. However, EPI-based design techniques may not be applicable in some cases, such as when a curved slice or an irregularly shaped region of interest is being imaged. Moreover, Cartesian k-space trajectories, such as used in EPI-based techniques, have been shown to be less SAR and RF power efficient than some non-Cartesian trajectories, such as spirals.
In contrast, the LCLTA design approach is more general than both the STA and EPI-based techniques, in part because there is no special requirement on the desired magnetization profile and a large class of non-Cartesian k-space trajectories can be used. The LCLTA approach generalizes the STA method so that initial magnetization can be arbitrary and larger flip angles can be created. This property allows designing a large-tip-angle pulse through concatenating a sequence of small-excitation pulses, when certain conditions or assumptions are met.
It would therefore be desirable to have a system and method capable of quickly producing multi-channel, multi-dimensional spatially selective RF pulse waveforms of arbitrary flip angles. It would be further desirable for such system and method to be general enough to account for arbitrary initial magnetizations and arbitrarily shaped magnetization profiles, e.g. by utilizing the LCLTA design approach.